Séminaire Lotharingien de Combinatoire, 93B.128 (2025), 12 pp.
Eugene Gorsky, Soyeon Kim, Tonie Scroggin and José Simental
Skew Shaped Positroids and Double Bott-Samelson Varieties
Abstract.
Skew shaped positroid varieties are subvarieties of the Grassmannian defined by determinantal equations, and are special cases of open positroid varieties. Double Bott-Samelson varieties are algebraic varieties defined in terms of configurations of flags depending on a positive braid word. We explicitly realize every skew shaped positroid in Gr(k,n) as a double Bott-Samelson variety, and use this to construct splicing maps for skew shaped positroid varieties, generalizing those constructed by the first and third authors in the case of maximal positroid cells.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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